research-article

On infinity norms as Lyapunov functions for piecewise affine systems

Authors:

Andrej JokićAuthors Info & Claims

HSCC '10: Proceedings of the 13th ACM international conference on Hybrid systems: computation and control

Pages 131 - 140

https://doi.org/10.1145/1755952.1755972

Published: 12 April 2010 Publication History

Abstract

This paper considers off-line synthesis of stabilizing static feedback control laws for discrete-time piecewise affine (PWA) systems. Two of the problems of interest within this framework are: (i) incorporation of the S-procedure in synthesis of a stabilizing state feedback control law and (ii) synthesis of a stabilizing output feedback control law. Tackling these problems via (piecewise) quadratic Lyapunov function candidates yields a bilinear matrix inequality at best. A new solution to these problems is proposed in this work, which uses infinity norms as Lyapunov function candidates and, under certain conditions, requires solving a single linear program. This solution also facilitates the computation of piecewise polyhedral positively invariant (or contractive) sets for discrete-time PWA systems.

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Cited By

Do HBlanchini FMiani SProdan I(2024)LP-Generated Control Lyapunov Functions With Application to Multicopter ControlIEEE Transactions on Control Systems Technology10.1109/TCST.2024.339670432:6(2090-2101)Online publication date: Nov-2024
https://doi.org/10.1109/TCST.2024.3396704
Palacios Roman JHafstein S(2024)Convex Lyapunov Functions for Switched Discrete-Time Systems by Linear Programming2024 25th International Carpathian Control Conference (ICCC)10.1109/ICCC62069.2024.10569580(01-06)Online publication date: 22-May-2024
https://doi.org/10.1109/ICCC62069.2024.10569580
Meijer TDolk VHeemels W(2024)Certificates of nonexistence for analyzing stability, stabilizability and detectability of LPV systemsAutomatica10.1016/j.automatica.2024.111841170(111841)Online publication date: Dec-2024
https://doi.org/10.1016/j.automatica.2024.111841
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Index Terms

On infinity norms as Lyapunov functions for piecewise affine systems
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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cover image ACM Conferences

HSCC '10: Proceedings of the 13th ACM international conference on Hybrid systems: computation and control

April 2010

308 pages

ISBN:9781605589558

DOI:10.1145/1755952

General Chairs:
Karl Henrik Johansson
KTH, Sweden
,
Wang Yi
Uppsala University, Sweden

Copyright © 2010 ACM.

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Published: 12 April 2010

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HSCC '10: The 13th ACM International Conference on Hybrid Systems: Computation and Control

April 12 - 15, 2010

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Cited By

Do HBlanchini FMiani SProdan I(2024)LP-Generated Control Lyapunov Functions With Application to Multicopter ControlIEEE Transactions on Control Systems Technology10.1109/TCST.2024.339670432:6(2090-2101)Online publication date: Nov-2024
https://doi.org/10.1109/TCST.2024.3396704
Palacios Roman JHafstein S(2024)Convex Lyapunov Functions for Switched Discrete-Time Systems by Linear Programming2024 25th International Carpathian Control Conference (ICCC)10.1109/ICCC62069.2024.10569580(01-06)Online publication date: 22-May-2024
https://doi.org/10.1109/ICCC62069.2024.10569580
Meijer TDolk VHeemels W(2024)Certificates of nonexistence for analyzing stability, stabilizability and detectability of LPV systemsAutomatica10.1016/j.automatica.2024.111841170(111841)Online publication date: Dec-2024
https://doi.org/10.1016/j.automatica.2024.111841
Hafstein S(2018)Fast Algorithms for Computing Continuous Piecewise Affine Lyapunov FunctionsSimulation and Modeling Methodologies, Technologies and Applications10.1007/978-3-030-01470-4_15(274-299)Online publication date: 21-Nov-2018
https://doi.org/10.1007/978-3-030-01470-4_15
Ghasemi MAfzalian A(2017)Robust tube-based MPC of constrained piecewise affine systems with bounded additive disturbancesNonlinear Analysis: Hybrid Systems10.1016/j.nahs.2017.04.00726(86-100)Online publication date: Nov-2017
https://doi.org/10.1016/j.nahs.2017.04.007
Gallieri MGallieri M(2016)Robust Tracking with Soft ConstraintsLasso-MPC – Predictive Control with ℓ1-Regularised Least Squares10.1007/978-3-319-27963-3_7(145-172)Online publication date: 31-Mar-2016
https://doi.org/10.1007/978-3-319-27963-3_7
Gallieri MGallieri M(2016)Version 2: LASSO MPC with Stabilising Terminal CostLasso-MPC – Predictive Control with ℓ1-Regularised Least Squares10.1007/978-3-319-27963-3_5(85-110)Online publication date: 31-Mar-2016
https://doi.org/10.1007/978-3-319-27963-3_5
Hafstein SGiesl P(2015)Review on computational methods for Lyapunov functionsDiscrete and Continuous Dynamical Systems - Series B10.3934/dcdsb.2015.20.229120:8(2291-2331)Online publication date: Aug-2015
https://doi.org/10.3934/dcdsb.2015.20.2291
Björnsson JGudmundsson SHafstein S(2015)Class library in C++ to compute Lyapunov functions for nonlinear systems∗∗Björnsson and Gudmundsson are supported by The Icelandic Research Fund, grant nr. 130677-052 and 152429-051 respectively.IFAC-PapersOnLine10.1016/j.ifacol.2015.09.28448:11(778-783)Online publication date: 2015
https://doi.org/10.1016/j.ifacol.2015.09.284
Brunner FLazar MAllgöwer FFráänzle MLygeros J(2014)Computation of piecewise affine terminal cost functions for model predictive controlProceedings of the 17th international conference on Hybrid systems: computation and control10.1145/2562059.2562108(1-10)Online publication date: 15-Apr-2014
https://dl.acm.org/doi/10.1145/2562059.2562108
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